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Cyclists Break World Records on Olympic
Velodrome Built with Mathematica
When cyclists recently broke Olympic
records 21 times and world records twice on the Stone Mountain Velodrome at
the 1996 Summer Olympic Games in Atlanta, skeptics swallowed their previous
criticisms of this one-of-a-kind racing track. Racing around the 250-meter,
steel-supported oval at over 40 miles an hour, cyclists discovered that
this track was indeed fast. What many didn't realize was that the track's
designers had their eyes on the clock far before the races began, when they
actually designed and built the track in record time with the help of
Mathematica.
"All calculations for the track's shape (based on Fresnel integrals) and
component specifications were done entirely in Mathematica," says designer
Chris Nadovich. "It would have taken a whole team of engineers months to do
all the calculations and analysis manually. It took me only a few weeks to
write my Mathematica program, and then it did all the calculations on my
486 in just three hours." Mathematica solved simultaneous systems of
symbolic equations to produce precise numerical descriptions of each and
every one of the 20,000-some pieces of steel on which the steeply banked
track surface would rest.
Nadovich believes this precision directly contributed to the racers'
record-breaking speeds on the track. It has to do with the pole line
(indicated by the black line you see painted on the track) that cyclists
follow to get the most efficient ride. "All other tracks have some
variation in that line, so riders waver about six inches up and down during
each lap," says Nadovich. "In my Mathematica model, that line was one of
the constraints, and I was able to design the whole track around it. I made
it completely flat--a 'zero bubble' pole line."
In fact, it was in large part due to Mathematica that amateur cyclists
Nadovich and Dale Hughes dared to submit their proposal for this
revolutionary track to the Atlanta Committee for the Olympic Games (ACOG)
in the first place. "Key to our winning the bid was price," explains
Nadovich, an electrical engineer by profession. Reducing the cost of the
project by several hundred thousand dollars is the fact that this track,
unlike any other official racing track in the world, is completely modular.
Now that the Games are over, the whole structure has been dismantled and either
stored or transported to a
new location. This eliminates the highly expensive demolition that would be
required for a traditional wooden track. "Given that the ACOG wanted the
venue removed and park restored to its natural state after the Games, ours
was the most economic concept," says Nadovich.
In addition to cost, the ACOG had to consider the fact that Nadovich and
Hughes had no prior world-class velodrome-building experience, whereas the
international leader in this business has been constructing velodromes for
over a hundred years. "I believe we overcame the Committee's reservations
because we were able to show so much detail in our proposal," says
Nadovich. "With Mathematica, I could write initial code for the model
quickly and generate numbers that could be read directly by a CAD drawing
program. I think the realistic three-dimensional visualizations helped
convince them we knew how to put this together exactly the way they wanted
it."
Want more details? Find out more
about the Olympic velodrome. You can also read about other interesting uses of Mathematica.
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